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Regularly weakly based modules over right perfect rings and Dedekind domains

Michal Hrbek, Pavel Růžička (2017)

Czechoslovak Mathematical Journal

A weak basis of a module is a generating set of the module minimal with respect to inclusion. A module is said to be regularly weakly based provided that each of its generating sets contains a weak basis. We study (1) rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, and (2) regularly weakly based modules over Dedekind domains.

Relative multiplication and distributive modules

José Escoriza, Blas Torrecillas (1997)

Commentationes Mathematicae Universitatis Carolinae

We study the construction of new multiplication modules relative to a torsion theory τ . As a consequence, τ -finitely generated modules over a Dedekind domain are completely determined. We relate the relative multiplication modules to the distributive ones.

Ring extensions with some finiteness conditions on the set of intermediate rings

Ali Jaballah (2010)

Czechoslovak Mathematical Journal

A ring extension R ⊆ S is said to be FO if it has only finitely many intermediate rings. R ⊆ S is said to be FC if each chain of distinct intermediate rings in this extension is finite. We establish several necessary and sufficient conditions for the ring extension R ⊆ S to be FO or FC together with several other finiteness conditions on the set of intermediate rings. As a corollary we show that each integrally closed ring extension with finite length chains of intermediate rings is necessarily a normal pair...

Some remarks on Prüfer modules

S. Ebrahimi Atani, S. Dolati Pishhesari, M. Khoramdel (2013)

Discussiones Mathematicae - General Algebra and Applications

We provide several characterizations and investigate properties of Prüfer modules. In fact, we study the connections of such modules with their endomorphism rings. We also prove that for any Prüfer module M, the forcing linearity number of M, fln(M), belongs to {0,1}.

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